






def 				A		(					lowercase__  :  int ,		lowercase__  :  int  )		-> int:
	UpperCamelCase__ :List[str]						=      1  # To kept the Calculated Value
	# Since C(n, k) = C(n, n-k)
	if k > (n - k):
		UpperCamelCase__ :Any						=      n - k
	# Calculate C(n,k)
	for i in range(lowercase__  ):
		result *= n - i
		result //= i + 1
	return result




def 				A		(					lowercase__  :  int  )		-> int:
	return binomial_coefficient(2 * node_count ,		lowercase__  ) // (node_count + 1)




def 				A		(					lowercase__  :  int  )		-> int:
	if n < 0:
		raise ValueError("""factorial() not defined for negative values"""  )
	UpperCamelCase__ :Union[str, Any]						=      1
	for i in range(1 ,		n + 1  ):
		result *= i
	return result




def 				A		(					lowercase__  :  int  )		-> int:
	return catalan_number(lowercase__  ) * factorial(lowercase__  )


if __name__ == "__main__":
							UpperCamelCase        =				int(input("Enter the number of nodes: ").strip() or 0)
							if node_count <= 0:
														raise ValueError("We need some nodes to work with.")
							print(
							    f'''Given {node_count} nodes, there are {binary_tree_count(node_count)} '''
							    f'''binary trees and {catalan_number(node_count)} binary search trees.'''
							)
"""simple docstring"""



from __future__ import annotations

import math



def 	_lowerCamelCase(	a   ,    a				):
       __a       =    u
       for i in range(1   ,    a				):
              __a       =    temp * (u - i)
       return temp



def 	_lowerCamelCase(	):
       __a       =    int(input("enter the numbers of values: "				)				)
       __a       =    []
       for _ in range(a				):
              y.append([]				)
       for i in range(a				):
              for j in range(a				):
                     y[i].append(a				)
                     __a       =    0

       print("enter the values of parameters in a list: "				)
       __a       =    list(map(a   ,    input().split()				)				)

       print("enter the values of corresponding parameters: "				)
       for i in range(a				):
              __a       =    float(input()				)

       __a       =    int(input("enter the value to interpolate: "				)				)
       __a       =    (value - x[0]) / (x[1] - x[0])

       # for calculating forward difference table

       for i in range(1   ,    a				):
              for j in range(n - i				):
                     __a       =    y[j + 1][i - 1] - y[j][i - 1]

       __a       =    y[0][0]
       for i in range(1   ,    a				):
              summ += (ucal(a   ,    a				) * y[0][i]) / math.factorial(a				)

       print(F"the value at {value} is {summ}"				)


if __name__ == "__main__":
   main()
